Shocks in the asymmetric simple exclusion process in a discrete-time update

We study the dynamics of a shock distribution as an initial state for a one -dimensional asymmetric simple exclusion process with sub-lattice parallel update. The time evolution of the shock distribution can be calculated exac tly if the two initial densities of the shock satisfy a special relation wh ich results from its U-q[SU(2)] symmetry. The resulting distribution is a l inear combination of shock measures. The motion of the shock position can b e interpreted as if it would perform a biased discrete-time random walk, wi th hopping rules related to that of a single particle in the exclusion proc ess. The shock diffusion constant and the shock velocity are calculated exa ctly. We obtain simple expressions for these quantities in terms of the sho ck densities and currents which we argue to be valid for any pair of shock densities.